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natima [27]
3 years ago
13

The vertex of this parabola is at (-2,-3). When the y-value is -2, the x-value is -5. What is the coefficient of the squared ter

m in the parabola's equation? 5 re (-2, -3)​
Mathematics
1 answer:
ra1l [238]3 years ago
3 0

Answer:

The coefficient of the squared term of the equation is 1/9.

Step-by-step explanation:

We are given that the vertex of the parabola is at (-2, -3). We also know that when the <em>y-</em>value is -2, the <em>x-</em>value is -5. Using this information we want to find the cofficient of the squared term in the parabola's equation.

Since we are given the vertex, we can use the vertex form:

\displaystyle y=a(x-h)^2+k

Where <em>a</em> is the leading coefficient and (<em>h, k</em>) is the vertex.

Since the vertex is (-2, -3), <em>h</em> = -2 and <em>k</em> = -3:

\displaystyle y=a(x-(-2))^2+(-3)

Simplify:

y=a(x+2)^2-3

We are also given that <em>y</em> = -2 when <em>x</em> = -5. Substitute:

(-2)=a(-5+2)^2-3

Solve for <em>a</em>. Simplify:

\displaystyle \begin{aligned} -2&=a(-3)^2-3\\ 1&=9a \\a&=\frac{1}{9}\end{aligned}

Therefore, our full vertex equation is:

\displaystyle y=\frac{1}{9}(x+2)^2-3

We can expand:

\displaystyle y=\frac{1}{9}(x^2+4x+4)-3

Simplify:

\displaystyle y=\frac{1}{9}x^2+\frac{4}{9}x-\frac{23}{9}

The coefficient of the squared term of the equation is 1/9.

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